A cross-flow heat exchanger unit comprising a plurality of corrugated film elements stacked in alternating layers such that the ridges and grooves of each film element extend transversely to those of an adjacent film element. Flat divider elements are interposed between each pair of adjacent film elements, and the structure is enclosed by a coating which bonds the elements together to form a rigid heat exchanger block. The film elements may be of non-metallic material, and the coating may be a curable, synthetic resinous material.